Compute Probabilities of a Poisson Random Variable
-The number of goals scored at State College hockey games follows a Poisson distribution with a mean of 4 goals per game. Find the probability that each of three randomly selected State College hockey games resulted in five goals being scored.
A) 0.00381788
B) 0.46888038
C) 0.00028461
D) 0.53111962

Question

Quizplus · Accepted Answer

The probability of a specific number of events (k) happening in a fixed interval of time or space in a Poisson distribution is given by the formula P(k; λ) = (e^(-λ) * λ^k) / k!, where λ is the average number of events (mean) and k is the number of occurrences of the event. Here, λ = 4 (mean number of goals) and k = 5 (number of goals we're interested in). So, for one game, the probability P(5; 4) = (e^(-4) * 4^5) / 5! = 0.15629345. Since the question asks for the probability of this happening in each of three randomly selected games, and assuming each game is independent, we multiply the probability of one game by itself three times: 0.15629345^3 = 0.00381788.